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10. Problem 11.80E(HRW) A thin rod of length l and mass m is suspended freely from
one end. It is pulled to one side and then allowed to swing like a pendulum,
passing through its lowest position with an angular speed
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. (a) Calculate its
kinetic energy as it passes through its lowest position. (b) How high
does its centre of mass rise above its lowest position? Neglect friction and air
resistance.|
Solution: Click For PDF Version
(a) Let the mass of the rod of length
(b) Let
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be
. Its moment of inertia,
, about the axis perpendicular
to its plane of oscillation and passing through its upper end will be
. As the angular speed of the
swinging rod at its lowest position is
, the kinetic energy of the rod
as it passes through its lowest position will be
be the
maximum angle that the rod makes with the vertical during its swing. At this
position the kinetic energy of the rod will be zero and its potential energy
will be determined by the change in height,
, of the centre of mass from its
lowest position. 
By equating the change in
potential energy to change in kinetic energy, we can find,
